{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculations with Reference States\n",
    "\n",
    "## Experimental Reference States: Formation and Mixing Energy\n",
    "\n",
    "By default, energies calculated with pycalphad (e.g. `GM`, `HM`, etc.) are the absolute energies as defined in the database and are not calculated with respect to any reference state.\n",
    "\n",
    "pycalphad `Model` objects allow the reference for the pure components to be set to arbitrary phases and temperature/pressure conditions through the `shift_reference_state` method, which creates new properties for the energies that are referenced to the new reference state, `GMR`, `HMR`, `SMR`, and `CPMR`.\n",
    "\n",
    "### Enthalpy of mixing\n",
    "\n",
    "The enthalpy of mixing in the liquid, analogous to what would be measured experimentally, is calculated and plotted below with the reference states of the pure elements both set to the liquid phase. No temperature and pressure are specified as we would like the reference state to be calculated with respect to the calculation temperature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pycalphad import Database, calculate, Model, ReferenceState, variables as v\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "dbf = Database(\"nbre_liu.tdb\")\n",
    "comps = [\"NB\", \"RE\", \"VA\"]\n",
    "\n",
    "# Create reference states\n",
    "Nb_ref = ReferenceState(\"NB\", \"LIQUID_RENB\")\n",
    "Re_ref = ReferenceState(\"RE\", \"LIQUID_RENB\")\n",
    "liq_refstates = [Nb_ref, Re_ref]\n",
    "\n",
    "# Create the model and shift the reference state\n",
    "mod_liq = Model(dbf, comps, \"LIQUID_RENB\")\n",
    "mod_liq.shift_reference_state(liq_refstates, dbf)\n",
    "calc_models = {\"LIQUID_RENB\": mod_liq}\n",
    "\n",
    "# Calculate HMR for the liquid at 2800 K from X(RE)=0 to X(RE)=1\n",
    "conds = {v.P: 101325, v.T: 2800, v.X(\"RE\"): (0, 1, 0.01)}\n",
    "result = calculate(dbf, comps, \"LIQUID_RENB\", P=101325, T=2800, output=\"HMR\", model=calc_models)\n",
    "\n",
    "# Plot\n",
    "fig = plt.figure(figsize=(9,6))\n",
    "ax = fig.gca()\n",
    "ax.scatter(result.X.sel(component='RE'), result.HMR, marker='.', s=5, label='LIQUID')\n",
    "ax.set_xlim((0, 1))\n",
    "ax.set_xlabel('X(RE)')\n",
    "ax.set_ylabel('HM_MIX')\n",
    "ax.set_title('Nb-Re LIQUID Mixing Enthalpy')\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Enthalpy of formation - convex hull\n",
    "\n",
    "Formation enthalpies are often reported in the literature with respect to the pure elements in their stable phase at 298.15 K. The enthalpy of formation of the phases in equilibrium, analogous to what would be measured experimentally, is calculated and plotted below for T=2800 K, with the reference states of the pure elements both set to the stable phases and fixed at 298.15 K and 1 atm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pycalphad import Database, equilibrium, Model, ReferenceState, variables as v\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "dbf = Database(\"nbre_liu.tdb\")\n",
    "comps = [\"NB\", \"RE\", \"VA\"]\n",
    "phases = dbf.phases.keys()\n",
    "\n",
    "# Create reference states\n",
    "Nb_ref = ReferenceState(\"NB\", \"BCC_RENB\", {v.T: 298.15, v.P: 101325})\n",
    "Re_ref = ReferenceState(\"RE\", \"HCP_RENB\", {v.T: 298.15, v.P: 101325})\n",
    "\n",
    "# Create the models for each phase and shift them all by the same reference states.\n",
    "eq_models = {}\n",
    "for phase_name in phases:\n",
    "    mod = Model(dbf, comps, phase_name)\n",
    "    mod.shift_reference_state([Nb_ref, Re_ref], dbf)\n",
    "    eq_models[phase_name] = mod\n",
    "\n",
    "# Calculate HMR at 2800 K from X(RE)=0 to X(RE)=1\n",
    "conds = {v.P: 101325, v.T: 2800, v.X(\"RE\"): (0, 1, 0.01)}\n",
    "result = equilibrium(dbf, comps, phases, conds, output=\"HMR\", model=eq_models)\n",
    "\n",
    "# Find the groups of unique phases in equilibrium e.g. [CHI_RENB] and [CHI_RENB, HCP_RENB]\n",
    "unique_phase_sets = np.unique(result.Phase.values.squeeze(), axis=0)\n",
    "\n",
    "# Plot\n",
    "fig = plt.figure(figsize=(9,6))\n",
    "ax = fig.gca()\n",
    "for phase_set in unique_phase_sets:\n",
    "    label = '+'.join([ph for ph in phase_set if ph != ''])\n",
    "    # composition indices with the same unique phase\n",
    "    unique_phase_idx = np.nonzero(np.all(result.Phase.values.squeeze() == phase_set, axis=1))[0]\n",
    "    masked_result = result.isel(X_RE=unique_phase_idx)\n",
    "    ax.plot(masked_result.X_RE.squeeze(), masked_result.HMR.squeeze(), marker='.', label=label)\n",
    "ax.set_xlim((0, 1))\n",
    "ax.set_xlabel('X(RE)')\n",
    "ax.set_ylabel('HM_FORM')\n",
    "ax.set_title('Nb-Re Formation Enthalpy (T=2800 K)')\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Special `_MIX` Reference State\n",
    "\n",
    "pycalphad also includes special mixing reference state that is referenced to the endmembers for that phase with the `_MIX` suffix (`GM_MIX`, `HM_MIX`, `SM_MIX`, `CPM_MIX`). This is particularly useful for seeing how the mixing contributions from physical or excess models affect the energy. The `_MIX` properties are set by default and no instantiation of `Model` objects and calling `shift_reference_state` is required.\n",
    "\n",
    "Below is an example for calculating this endmember-referenced mixing enthalpy for the $\\chi$ phase in Nb-Re. Notice that the four endmembers have a mixing enthalpy of zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pycalphad import Database, calculate\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "dbf = Database(\"nbre_liu.tdb\")\n",
    "comps = [\"NB\", \"RE\", \"VA\"]\n",
    "\n",
    "# Calculate HMR for the Chi at 2800 K from X(RE)=0 to X(RE)=1\n",
    "result = calculate(dbf, comps, \"CHI_RENB\", P=101325, T=2800, output='HM_MIX')\n",
    "\n",
    "# Plot\n",
    "fig = plt.figure(figsize=(9,6))\n",
    "ax = fig.gca()\n",
    "ax.scatter(result.X.sel(component='RE'), result.HM_MIX, marker='.', s=5, label='CHI_RENB')\n",
    "ax.set_xlim((0, 1))\n",
    "ax.set_xlabel('X(RE)')\n",
    "ax.set_ylabel('HM_MIX')\n",
    "ax.set_title('Nb-Re CHI Mixing Enthalpy')\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculations at specific site fractions\n",
    "\n",
    "In the previous example, the mixing energy for the CHI phase in Nb-Re is sampled by sampling site fractions linearly between endmembers and then randomly across site fraction space.\n",
    "\n",
    "Imagine now that you'd like to calculate the mixing energy along a single internal degree of freedom (i.e. between two endmembers), referenced to those endmembers.\n",
    "\n",
    "A custom 2D site fraction array can be passed to the `points` argument of `calculate` and the `HM_MIX` property can be calculated as above.\n",
    "\n",
    "The sublattice model for CHI is `RE : NB,RE : NB,RE`.\n",
    "\n",
    "If we are interested in the interaction along the second sublattice when NB occupies the third sublattice, we need to construct a site fraction array of \n",
    "\n",
    "```python\n",
    "# RE, NB, RE, NB, RE\n",
    "[ 1.0, x, 1-x, 1.0, 0.0 ]\n",
    "```\n",
    "\n",
    "where `x` varies from 0 to 1. This fixes the site fraction of RE in the first sublattice to 1 and the site fractions of NB and RE in the third sublattice to 1 and 0, respectively. Note that the site fraction array is sorted first in sublattice order, then in alphabetic order within each sublattice (e.g. NB is always before RE within a sublattice)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Site fractions:\n",
      "[[1.00e+00 1.00e-12 1.00e+00 1.00e+00 0.00e+00]\n",
      " [1.00e+00 1.00e-03 9.99e-01 1.00e+00 0.00e+00]\n",
      " [1.00e+00 2.00e-03 9.98e-01 1.00e+00 0.00e+00]\n",
      " ...\n",
      " [1.00e+00 9.98e-01 2.00e-03 1.00e+00 0.00e+00]\n",
      " [1.00e+00 9.99e-01 1.00e-03 1.00e+00 0.00e+00]\n",
      " [1.00e+00 1.00e+00 0.00e+00 1.00e+00 0.00e+00]]\n",
      "Site fractions shape: (1001, 5) (1001 points, 5 internal degrees of freedom)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pycalphad import Database, calculate\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "dbf = Database(\"nbre_liu.tdb\")\n",
    "comps = [\"NB\", \"RE\", \"VA\"]\n",
    "\n",
    "# The values for the internal degree of freedom we will vary\n",
    "n_pts = 1001\n",
    "x = np.linspace(1e-12, 1, n_pts)\n",
    "\n",
    "# Create the site fractions\n",
    "# The site fraction array is ordered first by sublattice, then alphabetically be species within a sublattice.\n",
    "# The site fraction array is therefore `[RE#0, NB#1, RE#1, NB#2, RE#2]`, where `#0` is the sublattice at index 0.\n",
    "# To calculate a RE:NB,RE:NB interaction requires the site fraction array to be [1, x, 1-x, 1, 0]\n",
    "# Note the 1-x is required for site fractions to sum to 1 in sublattice #1.\n",
    "site_fractions = np.array([np.ones(n_pts), x, 1-x, np.ones(n_pts), np.zeros(n_pts)]).T\n",
    "print('Site fractions:')\n",
    "print(site_fractions)\n",
    "print('Site fractions shape: {} ({} points, {} internal degrees of freedom)'.format(site_fractions.shape, site_fractions.shape[0], site_fractions.shape[1]))\n",
    "\n",
    "# Calculate HMR for the Chi at 2800 K from Y(CHI, 1, RE)=0 to Y(CHI, 1, RE)=1\n",
    "# Pass the custom site fractions to the `points` argument\n",
    "result = calculate(dbf, comps, \"CHI_RENB\", P=101325, T=2800, points=site_fractions, output='HM_MIX')\n",
    "# Extract the site fractions of RE in sublattice 1.\n",
    "Y_CHI_1_RE = result.Y.squeeze()[:, 2]\n",
    "\n",
    "# Plot\n",
    "fig = plt.figure(figsize=(9,6))\n",
    "ax = fig.gca()\n",
    "\n",
    "ax.scatter(Y_CHI_1_RE, result.HM_MIX, marker='.', s=5)\n",
    "ax.set_xlim((0, 1))\n",
    "ax.set_xlabel('Y(CHI, 1, RE)')\n",
    "ax.set_ylabel('HM_MIX')\n",
    "ax.set_title('Nb-Re CHI Mixing Enthalpy')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:calphad-dev-2]",
   "language": "python",
   "name": "conda-env-calphad-dev-2-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
